1. (W)Where (Understanding), Why (Real Life), What (MLR) and Product 2. (H)Hook (Engage) 3. (E)Equip (Content - Students will know...), Explore (Graphic Organizer), and Experience (Cooperative Learning) 4. (R)Rethink, Revise, Rehearse, and Refine (Timely Feedback) 5. (E)Evaluate (Self- Assessment) 6. (T) Tailor (Multiple Intelligences 6 to 8 and use each at least twice) 7. (O)Organize (Facet of Understanding - Students will be able to ...)
Lesson 1
Consider the W.H.E.R.E.T.O. elements. (L)
1. Students will understand that functions and graphs are related. (where) This lesson is important because students will learn how graphs and functions relate to the real world. (why) Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.(what) Product: Graphs depicting the velocity of an object from equations using spreadsheet.
2. Math rap video. (hook)
3. Students will know the definition of function, graph and equations (equip). I will use a step-by-step chart to help the students work on defining the formula for the velocity of a rolled ball. (explore) I will have the students work together to find the time it takes an object to roll a certain distance. (experience)
4. First I will allow students to discuss what they think will will happen (ball speed up, slow down, stay constant) and what each graph would look like. (rethink) Next I will have the students get into groups and have them roll balls and time them over certain distances and use the information to find a formula. (revise). Students will discuss what they found about velocity and formulas. (rehearse). I will collect the assignment and give feedback. (refine)
5. To evaluate I have the students find a formula for velocity and make a graph. (evaluate)
6. Verbal: By working with the definitions of words I will appeal to verbal students. Logical: By using math this lesson uses logical. Visual: The math rap at the beginning will be visual. Intrapersonal: The students are going to work alone for a while during class. Interpersonal: The group activity will help the students work together. Natural: We are finding the equation for velocity. Musical: The math rap will help engage the musical students.
7. Derive a graph from an equation. (explanation)
Lesson 2
Consider the W.H.E.R.E.T.O. elements. (L)
8. Functions and graphs are related. (where) This lesson will help students see that a graph can tell you a lot of information. (why)Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.(what) Product: T-charts and graphs using excel.
9. Funny saying/graph using all the concepts. (hook)
10. Student will know the definitions of range, zeros, intercepts, and maximum and minimum values. (equip) Students will use a T-chart to keep the different terms separate and to learn the information. (explore) When students have worked by themselves for a while I will have them do a circle the sage exercise. (experience)
11. First we will have a class discussion on the terms and get some idea of what the students think the words mean. (rethink) I will next have the students fill out a T-chart with the terminology. (revise) Students will then discuss the concepts with each other in the circle the sage. (rehearse) I will have the students use excel to figure out how to change a graph using the concepts discussed in the day. (refine)
12. By using excel the students will make graphs that fit certain parameters. (evaluate)
13. Verbal: The different concepts and definitions will appeal to verbal learners. Logical: By using math this lesson uses logical. Visual: Making the graphs will help the visual learners. Intrapersonal: The students will work alone for a while before working in groups. Interpersonal: The sage activity will allow students to talk among themselves. Physical: By using the sage activity the students will get up and move.
14. Use concepts such as range, zeros, intercepts, and maximums and minimum values. (application)
Lesson 3
Consider the W.H.E.R.E.T.O. elements. (L)
15. There is more than one way to solve an equation. (where) This lesson is important because it will help show students that there is more than one right way to solve a problem. (why) Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.(what) Product: Graphs made using excel and graphing calculators.
16. Power = work/time etc. (hook)
17. Students will learn vocabulary including slope and intercepts. (equip) They will use an observation chart to determine what changing m or b does to a graph. (explore) The students will use a three step interview to help fellow students that may be having trouble. (experience)
18. First we will discuss what the students think changing m and b will do to a graph. (rethink) Then the students will use an observation chart to learn what m and b do to a graph. (revise) Then the students will find a partner and discuss how they would make graphs look a certain way. (rehearse) The students will use excel to help them see what b and m do to a graph. (refine)
19. The students will be using excel to see how m and b effect a graph. (evaluate)
20. Verbal: By having the students learn the vocabulary I will get the verbal learners interested. Logical: By using math this lesson uses logical. Visual: The graphs provided by excel will help the visual learners. Intrapersonal: The activity where the students write their observation charts will be done alone. Interpersonal: When the students work with a partner and at the beginning of the class. Natural: I can help engage the natural learners by making references to slopes of hills and mountains. Physical: The physical students will stay engaged when they move around for group work.
21. Interpret the characteristics of functions using graphs, tables, and algebraic techniques (interpretation)
Lesson 4
Consider the W.H.E.R.E.T.O. elements. (L)
22. Functions and graphs are related. (where) This lesson is important because it will show students that there is more than one right way to solve a problem. (why)Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.(what) product- worksheet and SmartBoard
23. bad pun about graphs dating equations (hook)
24. Students will learn about more vocabulary. (equip) We will use a step-by-step worksheet to make some graphs from equations. (explore) Then students will use a think-pair-share discussion to talk about ideas with other people in the class. (experience)
25. I will have the students develop what they think the differences and similarities between graphs and equations are. (rethink) Then I will have them work on a sheet of equations. (revise) They will then talk about the equations and graphs with a partner. (rehearse) I will allow students to come up to the SmartBoard and put their ideas down as well as make some graphs. (refine)
26. I will use SmartBoard to introduce the topics and make graphs. (evaluate)
27. Verbal: I will help the verbal learners by dealing with vocabulary. Logical: By using math this lesson uses logical. Visual: Working on the SmartBoard will help the visual learners. Intrapersonal: Being able to work alone for a while will help the intrapersonal learners. Interpersonal: By working in pairs and then as the whole class the interpersonal learners will benefit. Physical: The physical learners will stay engaged because they will be getting up and moving to the SmartBoard.
28. Compare how graphs relate to equations (perspective)
Lesson 5
Consider the W.H.E.R.E.T.O. elements. (L)
29. There is more than one way to solve an equation. (where) This lesson is important because it will help students recognize the basic functions. (why) Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.(what) product: short quiz on the SmartBoard
30. xkcd comic (hook)
31. Students will learn the graphs of the basic functions. (equip) I will have the students work on T-charts to help understand each of the unique graphs. (explore) I will use a jigsaw group activity to allow the students time to work together. (experience)
32. First I will have the students guess which graph matches with which equation. (rethink) I will then have them work on T-charts to help them understand the different graphs. (revise) By using a jigsaw activity I will have my students discuss the graphs and work on a worksheet. (rehearse) Lastly the students will take a matching jeopardy quiz on the SmartBoard in teams of five. (refine)
33. I will use both the worksheet and the SmartBoard quiz to determine where the class is. (evaluate)
34. Logical: By using math this lesson uses logical. Visual: By doing a quiz on the SmartBoard I will engage the visual learners. Intrapersonal: I am having them work alone on the T-charts. Interpersonal: After working alone they are taking a jeopardy quiz in groups. Musical: During the jeopardy quiz I will have different sounds play. Natural: I will dicuss where some of the equations can be found in nature. Physical: I will include physical by having the students move around to answer the SmartBoard.
35. Recognize the graphs of the basic functions (self-knowledge)
Lesson 6
Consider the W.H.E.R.E.T.O. elements. (L)
36. Graphs are useful in the real world. (where) This lesson is important because it links graphs to the real world. (why)Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.(what) Product- Stock Graph/Presentation - wikispace.
37. xkcd comic (hook)
38. Students will use terminology that we have already covered and expand on it. (equip) They will work on an idea wheel to help them gather their thoughts on how graphs are useful in the real world. (exlpore) The students will use a round robin activity to share their ideas. (experience)
39. First students will think about ways that they think graphs can be used in real life. (rethink) Next they will work on their idea wheel. (revise) They will discuss these wheels in a round robin fashoin. (rehearse) Then they will give presentations that we have been working on for a while. (refine)
40. I will use their presentations to evaluate them. (evaluate)
41. Verbal: The presentation will be good for verbal people. Logical: By using math this lesson uses logical. Visual: In the presentation the students have to provide graphs. Intrapersonal: At the beginning of the class they are going to work independently for a little bit. Interpersonal: The round robin activity will be interpersonal Physical: During the presentation they will have to get up and move around.
42. Consider how graphs are used in the real world. (organize)
Stage 3 Plan Learning Experiences and Instruction
1. (W) Where (Understanding), Why (Real Life), What (MLR) and Product
2. (H) Hook (Engage)
3. (E) Equip (Content - Students will know...), Explore (Graphic Organizer), and Experience (Cooperative Learning)
4. (R) Rethink, Revise, Rehearse, and Refine (Timely Feedback)
5. (E) Evaluate (Self- Assessment)
6. (T) Tailor (Multiple Intelligences 6 to 8 and use each at least twice)
7. (O) Organize (Facet of Understanding - Students will be able to ...)
Lesson 1
2. Math rap video. (hook)
3. Students will know the definition of function, graph and equations (equip). I will use a step-by-step chart to help the students work on defining the formula for the velocity of a rolled ball. (explore) I will have the students work together to find the time it takes an object to roll a certain distance. (experience)
4. First I will allow students to discuss what they think will will happen (ball speed up, slow down, stay constant) and what each graph would look like. (rethink) Next I will have the students get into groups and have them roll balls and time them over certain distances and use the information to find a formula. (revise). Students will discuss what they found about velocity and formulas. (rehearse). I will collect the assignment and give feedback. (refine)
5. To evaluate I have the students find a formula for velocity and make a graph. (evaluate)
6. Verbal: By working with the definitions of words I will appeal to verbal students.
Logical: By using math this lesson uses logical.
Visual: The math rap at the beginning will be visual.
Intrapersonal: The students are going to work alone for a while during class.
Interpersonal: The group activity will help the students work together.
Natural: We are finding the equation for velocity.
Musical: The math rap will help engage the musical students.
7. Derive a graph from an equation. (explanation)
Lesson 2
9. Funny saying/graph using all the concepts. (hook)
10. Student will know the definitions of range, zeros, intercepts, and maximum and minimum values. (equip) Students will use a T-chart to keep the different terms separate and to learn the information. (explore) When students have worked by themselves for a while I will have them do a circle the sage exercise. (experience)
11. First we will have a class discussion on the terms and get some idea of what the students think the words mean. (rethink) I will next have the students fill out a T-chart with the terminology. (revise) Students will then discuss the concepts with each other in the circle the sage. (rehearse) I will have the students use excel to figure out how to change a graph using the concepts discussed in the day. (refine)
12. By using excel the students will make graphs that fit certain parameters. (evaluate)
13. Verbal: The different concepts and definitions will appeal to verbal learners.
Logical: By using math this lesson uses logical.
Visual: Making the graphs will help the visual learners.
Intrapersonal: The students will work alone for a while before working in groups.
Interpersonal: The sage activity will allow students to talk among themselves.
Physical: By using the sage activity the students will get up and move.
14. Use concepts such as range, zeros, intercepts, and maximums and minimum values. (application)
Lesson 3
16. Power = work/time etc. (hook)
17. Students will learn vocabulary including slope and intercepts. (equip) They will use an observation chart to determine what changing m or b does to a graph. (explore) The students will use a three step interview to help fellow students that may be having trouble. (experience)
18. First we will discuss what the students think changing m and b will do to a graph. (rethink) Then the students will use an observation chart to learn what m and b do to a graph. (revise) Then the students will find a partner and discuss how they would make graphs look a certain way. (rehearse) The students will use excel to help them see what b and m do to a graph. (refine)
19. The students will be using excel to see how m and b effect a graph. (evaluate)
20. Verbal: By having the students learn the vocabulary I will get the verbal learners interested.
Logical: By using math this lesson uses logical.
Visual: The graphs provided by excel will help the visual learners.
Intrapersonal: The activity where the students write their observation charts will be done alone.
Interpersonal: When the students work with a partner and at the beginning of the class.
Natural: I can help engage the natural learners by making references to slopes of hills and mountains.
Physical: The physical students will stay engaged when they move around for group work.
21. Interpret the characteristics of functions using graphs, tables, and algebraic techniques (interpretation)
Lesson 4
23. bad pun about graphs dating equations (hook)
24. Students will learn about more vocabulary. (equip) We will use a step-by-step worksheet to make some graphs from equations. (explore) Then students will use a think-pair-share discussion to talk about ideas with other people in the class. (experience)
25. I will have the students develop what they think the differences and similarities between graphs and equations are. (rethink) Then I will have them work on a sheet of equations. (revise) They will then talk about the equations and graphs with a partner. (rehearse) I will allow students to come up to the SmartBoard and put their ideas down as well as make some graphs. (refine)
26. I will use SmartBoard to introduce the topics and make graphs. (evaluate)
27. Verbal: I will help the verbal learners by dealing with vocabulary.
Logical: By using math this lesson uses logical.
Visual: Working on the SmartBoard will help the visual learners.
Intrapersonal: Being able to work alone for a while will help the intrapersonal learners.
Interpersonal: By working in pairs and then as the whole class the interpersonal learners will benefit.
Physical: The physical learners will stay engaged because they will be getting up and moving to the SmartBoard.
28. Compare how graphs relate to equations (perspective)
Lesson 5
30. xkcd comic (hook)
31. Students will learn the graphs of the basic functions. (equip) I will have the students work on T-charts to help understand each of the unique graphs. (explore) I will use a jigsaw group activity to allow the students time to work together. (experience)
32. First I will have the students guess which graph matches with which equation. (rethink) I will then have them work on T-charts to help them understand the different graphs. (revise) By using a jigsaw activity I will have my students discuss the graphs and work on a worksheet. (rehearse) Lastly the students will take a matching jeopardy quiz on the SmartBoard in teams of five. (refine)
33. I will use both the worksheet and the SmartBoard quiz to determine where the class is. (evaluate)
34. Logical: By using math this lesson uses logical.
Visual: By doing a quiz on the SmartBoard I will engage the visual learners.
Intrapersonal: I am having them work alone on the T-charts.
Interpersonal: After working alone they are taking a jeopardy quiz in groups.
Musical: During the jeopardy quiz I will have different sounds play.
Natural: I will dicuss where some of the equations can be found in nature.
Physical: I will include physical by having the students move around to answer the SmartBoard.
35. Recognize the graphs of the basic functions (self-knowledge)
Lesson 6
37. xkcd comic (hook)
38. Students will use terminology that we have already covered and expand on it. (equip) They will work on an idea wheel to help them gather their thoughts on how graphs are useful in the real world. (exlpore) The students will use a round robin activity to share their ideas. (experience)
39. First students will think about ways that they think graphs can be used in real life. (rethink) Next they will work on their idea wheel. (revise) They will discuss these wheels in a round robin fashoin. (rehearse) Then they will give presentations that we have been working on for a while. (refine)
40. I will use their presentations to evaluate them. (evaluate)
41. Verbal: The presentation will be good for verbal people.
Logical: By using math this lesson uses logical.
Visual: In the presentation the students have to provide graphs.
Intrapersonal: At the beginning of the class they are going to work independently for a little bit.
Interpersonal: The round robin activity will be interpersonal
Physical: During the presentation they will have to get up and move around.
42. Consider how graphs are used in the real world. (organize)
2004 ASCD and Grant Wiggins and Jay McTighe